In Exercises 5–8, use the following two control charts that re...

Question

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

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Is the process mean within statistical control? Why or why not?

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Is the process mean within statistical control? Why or why not?

Accepted Answer

Hello, everyone. Let's take a look at this question together. Use the following control chart, which results from the temperature deviation data for 25 consecutive batches, each containing 40 newly manufactured thermometers. The thermometers must meet strict accuracy standards. The recorded Values represent temperature deviations in degrees Celsius from a calibrated reference under controlled conditions. Industry regulations require that deviations remain within plus or minus 1.5 °C, and here we have our control chart for temperature deviations in thermometers, and we have to determine is the process within statistical control? Why or why not? Is it answer choice A? The process is within statistical control, as all points fall within control limits. Answer choice B, the process is within statistical control because none of the three out of control criteria are met. Answer choice C. The process is statistically out of control because there are points lying outside the control limits, or answer choice D, the process is out of control because of a consistent upward trend showing signs of deterioration. So in order to solve this question, we must first recall how we can determine if a process is within statistical control by. a control chart to determine which of the following answer choices is the correct answer. And we know that in order to determine whether the temperature deviation is within statistical control, we must analyze the control chart based on the three standard out of control criteria, which the first criteria is any point outside of the control limits. The second criteria is a run of consecutive points on one side of the center line, and the third criteria is a trend of increasing or decreasing values over several points. So, if our control chart for temperature deviation in thermometers meets any of the 3 standard out of control criteria, the process is out of statistical control. So, starting with the first standard of of out of control criteria, which is any point is outside of the control limits, we know from our control chart, the upper control limit is + 1.5 °C. The lower control limit is -1.5 °C, and our center line is 0 °C. So looking at our control chart for temperature deviations in thermometer, where we have Our upper control limit, our center line, and our lower control limit, we can identify that we have two points that are outside of our control limits, as 1 point exceeds the upper control limit and 1 point falls below the lower control limit. Therefore, we meet the criteria for the first standard, and then for the second standard, which is a run of consecutive points on one side of the standard. Line, we can see from our control chart that no 8 or more consecutive points are above or below the center line. Therefore, we do not meet the criteria for the second standard. And lastly, the third standard, which is a trend of increasing or decreasing values over several points, we are looking for a consistent upward or downward trend, which may indicate deterioration, however, from our control chart. We can identify, we do not meet this criteria. Therefore, we only meet the first standard out of control criteria, as there are points that are outside of the control limits. And so looking at our answer choices, we can identify that the correct answer choice is answer choice C. as answer choice C says that the process is statistically out of control because there are points lying outside of the control limits. Though answer choice C is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Control Charts

Process Mean

Statistical Control

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